Unit 16 – Statistics



Geometry and Finite Math Honors

Unit 16 – Statistics

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|DAY |TOPIC(S) |ASSIGNMENT |

| | | |

|1 |Measures of Center and Boxplots |HW 1 |

| | | |

|2 |Measures of Spread |HW 2 |

| |Standard Deviation | |

| | | |

|3 |Histograms and |HW 3 |

| |Measures of Position | |

| |z-scores | |

| | | |

|4 |The Normal Distribution |HW 4 |

| |& The Empirical Rule | |

| | | |

|5 |The Normal Distribution |HW 5 |

| |(Normal Calculations) | |

| | | |

|6 |Review |Review Packet |

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|7 |Unit 16 Test | |

Revised 4/15/14

Geo H Unit 16 – Day 1; Measures of Center and Boxplots

[pic]

(Label the axis with names and numbers.)

(a fancy way of asking for the “mean”)

4. Find the 5 – number summary for the price per month cost, and for the rank of the toothpaste brands listed in the table below. Create 2 boxplots (include labeled axes with names and numbers.) Write a few sentences comparing the centers, shapes and spreads of the graphs.

5.

Geo H Unit 16 – Day 2; Measures of Spread: Standard Deviation

1. Calculate the range, the standard deviation and the IQR for both Juneau and New York, using your graphing calculator (not with the formula – use STAT Calc, 1 Var Stats.) Which city has more variability in temperature? Explain your answer.

2. a. Given the deviations from the mean for Penny Saved’s bank account during the last 8

months are 0, -40, -78, -71, 33, 36, 42, 91, how do you know that at leas one of the

deviations is incorrect?

b. If it turns out that 33 is incorrect, while the others are correct, what should that deviation be?

c. Use the deviations to finish the calculation for the standard deviation. Square the deviations,

sum the results, divide the total by the number of deviations, and take the square root. Show

your work.

3.

4.

5. Which of the following histograms has the largest standard deviation? Which has the smallest? Explain your answer. Assume all graphs are on the same scale.

Geo H Unit 16 – Day 3; Histograms and Measures of Position (z-scores)

1.

a. The median cost is in which interval on the graph?

b. How many colleges cost between $3,000 and $3,500?

c. Is a college that costs $3,000 included in the above count? Is $3,500?

d. From the data, what percent of colleges cost $6,000 or more?

2. Noah and Rita are working on a report for economics.

They surveyed 95 farmers and recorded the number

of acres of corn they had planted. The histogram

displays the data they collected.

a. Describe the shape of the distribution.

b. How many farmers planted less than 2

acres of corn?

c. What percent of farmers planted less

than 2 acres of corn?

d. Estimate the median number of acres of corn planted.

e. Do you think the mean number of acres of corn planted is higher, lower, or about the

same as the median? Explain.

3. At a large university, 1500 students took a final exam in chemistry. Frank Stein learned that his

score of 76, placed him in the 88th percentile of test takers.

a. Roughly how many students scored lower than Frank?

b. Roughly how many students scored the same or higher than Frank?

c. Mary was placed at the 95th percentile of test takers. Describe how she performed on the test relative to Frank.

d. The highest score on the test was a 91. What is the percentile rank of this student?

4. Calculate the appropriate z-scores to answer the following question:

5.

Geo H Unit 16 – Day 4; The Normal Distribution and the Empirical Rule

1. Assume the mean height of an adult male gorilla is 68 in, with a standard deviation of 2.8 in.

a. Sketch a normal curve, with the mean

and 1, 2 and 3 standard deviations from

the mean clearly indicated.

b. What percent of adult male gorillas fall within one standard deviation of the mean?

c. Two?

d. Three?

2. Sketch a normal curve to answer the following question:

3.

4.

a. Draw a normal curve with one standard

deviation from the mean clearly indicated.

b. What is the mean ph level?

c. What is the standard deviation of ph levels?

d. 99.7% of ph levels fall within what range?

5.

a. Draw a normal curve with one, 2 and 3 standard deviations clearly indicated.

b. What percent of waiting times are less than 17 minutes?

c. What percent of waiting times are between 17 and 25 minutes?

d. What percent of waiting times are greater than 41 minutes?

e. What percent of waiting times are between 17 and 41 minutes?

f. What percent of waiting times are between 25 and 41 minutes?

g. How many minutes are the shortest 2.5% of waiting times?

Geo H Unit 16 – Day 5; The Normal Distribution (Normal Calculations)

Draw a normal curve for each set of problems. Show all work!

1.

2.

3.

Find this percentage of people.

4. The scores of a reference population on the Wechsler Intelligence Scale for Children (WISC)

are approximately Normally distributed with a mean of 100 and a standard deviation of 15. Draw the normal curve with one, two and three standard deviations clearly indicated on the graph.

(a) What score would represent the 50th percentile? Explain.

(b) What proportion of the reference population has WISC scores below 110? What percentile does this score represent? Explain in a sentence.

(c) What score would represent the 80th percentile? Explain.

(d) A score in what range would represent the top 1% of the scores?

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